Logistic Regression Overview

Logistic regression makes use of the sigmoid function which outputs a probability between 0 and 1. The sigmoid function with some weight parameter $\theta$ and some input $x^{(i)}$ is defined as follows.

Note that as $\theta^Tx^{(i)}$ gets closer and closer to $-\infty$ the denominator of the sigmoid function gets larger and larger and as a result, the sigmoid gets closer to $0$. On the other hand, as $\theta^Tx^{(i)}$ gets closer and closer to $\infty$ the denominator of the sigmoid function gets closer to 1 and as a result the sigmoid also gets closer to $1$.

Now given a tweet, you can transform it into a vector and run it through your sigmoid function to get a prediction as follows: